Mathematical analysis of models for the transmission dynamics of mosquito borne diseases

Abstract

Mosquitoes are long-legged, two winged flies that are responsible for the transmission of many diseases such as Zika fever, malaria, yellow fever, chikungunya and dengue

hemorrhagic fever. Mosquito borne diseases account for substantial amount of para- sitic and infectious diseases, they have profound effects on economic growth of many

developing countries. There have been continuous efforts to optimize and improve on existing mosquito control strategies, as well as to develop new tools aimed at reducing burden of mosquito borne diseases. Control strategies are either applied alone or in combination depending on available resources, education, health risk and burden of the disease.

The main aim of this thesis is to mathematically study three mosquito borne dis- eases in the presence of control, the diseases are Zika fever (this is because, in addition

to the disease being transmitted vertically, it is the first mosquito borne disease known to be transmitted sexually), yellow fever (because despite having effective vaccine for the disease, it has continue to pose sporadic challenges in different regions of the world), and malaria (because it has the highest global burden among mosquito borne diseases despite continuous efforts to eradicate it). Some major highlights of the thesis include: Roles of mosquito vertical transmission in the transmission dynamics of mosquito borne diseases, and effects of incorporating human-human transmission are evaluated. Assessment of impact of using different control measures both in human and mosquito populations, and effects of controlling population of adult male (non-disease transmitting) mosquitoes through sterilization are conducted. Implication of incorporating aquatic stage of mosquito development in models for the transmission of mosquito borne diseases, as well as effect of temperature variation in the transmission dynamics of malaria are also studied. In Chapter 1, brief introduction to the epidemiology of mosquito borne diseases

is presented. Basic results and definitions in mathematical epidemiology are also dis- cussed. In addition, some important mathematical theories and definitions used in

subsequent chapters are also presented. A Zika model that incorporates vectorial ver- tical transmission, human-human horizontal transmission, as well as human-mosquito

and mosquito-human transmissions is studied in Chapter 2. Another Zika model is considered in Chapter 3, the model incorporated human-human transmission in the

presence of mosquito sterilization. In Chapter 4, a yellow fever model with vaccina- tion, use of bed nets and mosquito control at both aquatic and non-aquatic stages

is constructed and analysed. Chapter 5 considered a temperature dependent malaria model in the presence of control. General conclusion is given in Chapter 6.